This Article 
 Bibliographic References 
 Add to: 
Approximate Throughput Computation of Stochastic Marked Graphs
July 1994 (vol. 20 no. 7)
pp. 526-535

A general iterative technique for approximate throughput computation of stochastic strongly connected marked graphs is presented. It generalizes a previous technique based on net decomposition through a single input-single output cut, allowing the split of the model through any cut. The approach has two basic foundations. First, a deep understanding of the qualitative behavior of marked graphs leads to a general decomposition technique. Second, after the decomposition phase, an iterative response time approximation method is applied for the computation of the throughput. Experimental results on several examples generally have an error of less than 3%. The state space is usually reduced by more than one order of magnitude; therefore, the analysis of otherwise intractable systems is possible.

[1] S. C. Agrawal, J. P. Buzen, and A. W. Shum, "Response time preservation: A general technique for developing approximate algorithms for queueing networks," inProc. ACM Sigmetrics Conf., Cambridge, MA, Aug. 21-24, 1984, pp. 63-77.
[2] A. Aho, J. Hopcroft, and J. Ullman,Data Structures and Algorithms. Reading, MA: Addison-Wesley, 1983.
[3] M. Ajmone Marsan, G. Balbao, and G. Conte,Performance Modeling of Multiprocessor Systems. Cambridge, MA: MIT Press, 1986.
[4] H. H. Ammar and S. M. R. Islam, "Time scale decomposition of a class of generalized stochastic Petri net models,"IEEE Trans. Software Eng.vol. 15, no. 6, pp. 809-820, June 1989.
[5] F. Baccelli and Z. Liu, "Comparison properties of stochastic decision free Petri nets,"IEEE Trans. Automat. Contr., vol. 37, no. 12, pp. 1905-1920, Dec. 1992.
[6] B. Baynat and Y. Dallery, "Approximate techniques for general closed queueing networks with subnetworks having population constraints," Tech. Rep.. MASI 90-49, Univ. Paris 6, Paris, France, Oct. 1990.
[7] B. Baynat and Y. Dallery, "A unified view of product-form approximation techniques for general closed queueing networks," Tech. Rep.. MASI 90-48, Univ. Paris 6, Paris, France, Oct. 1990.
[8] J. Campos, G. Chiola, J. M. Colom, and M. Silva, "Properties and performance bounds for timed marked graphs,"IEEE Trans. Circuits and Syst.--1: Fundamental Theory and Applicat., vol. 39, no. 5, pp. 386-401, May 1992.
[9] G. Chiola, "A graphical Petri net tool for performance analysis," inProc 3rd Int. Workshop on Modeling Tech. and Perform. Eval., AFCET, Paris, France, March 1987.
[10] G. Ciardo and K. S. Trivedi, "A decomposition approach for stochastic Petri net models," inProc. Fifth Int. Conf. Petri Net Models, Dec. 1991.
[11] J. M. Colom, "Análisis Estructural de Redes de Petri, Programación Lineal y Geometría Convexa," Ph.D. thesis, Dpto. de Ingeniería Eléctrica e Informática, Univ. Zaragoza, Spain, June 1989.
[12] J. M. Colom and M. Silva, "Improving the linearly based characterization of P/T nets," inAdvances in Petri Nets 1990, G. Rozenbeg, Ed. Berlin: Springer-Verlag, 1991, vol. 483 ofLNCS, pp. 113-145.
[13] Y. Dallery, Z. Liu, and D. Towsley, "Equivalence, reversibility and symmetry properties in fork/join queueing networks with blocking," Tech. Rep., MASI 90-32, Univ. Paris 6, Paris, France, June 1990.
[14] A. Desrochers, H. Jungnitz, and M. Silva, "An approximation method for the performance analysis of manufacturing systems based on GSPN's," inProc. Rensselaer's Third Int. Conf. Comput. Integ. Mfg., Troy, NY, May 1992, IEEE Comput. Soc. Press, pp. 46-55.
[15] S. Donatelli and M. Sereno, "On the product form solution for stochastic Petri nets," inProc. 13th Int. Conf. Applicat. and Theory of Petri NetsSheffield, UK, June 1992, pp. 154-172.
[16] H. Jungnitz, B. Sánchez, and M. Silva, "Approximate throughput computation of stochastic marked graphs,"J. Parallel and Distrib. Comput., vol. 15, pp. 282-295, 1992.
[17] H. J. Jungnitz, "Approximation Methods for Stochastic (Petri) Nets," Ph.D. thesis. Dept. of Elec., Comput. and Syst. Eng., Rensselaer Polytechnic Inst., Troy, NY, May 1992.
[18] Y. Li and C. M. Woodside, "Iterative decomposition and aggregation of stochastic marked graphs Petri nets," inProc. 12th Int. Conf. on Applicat. and Theory of Petri Nets, Gjern. Denmark, June 1991, pp. 257-275.
[19] Y. Li and C. M. Woodside, "Performance Petri net analysis of communications protocol software by delay-equivalent aggregation," inProc. 4th Int. Workshop on Petri Nets and Perform. Models, Melbourne, Australia, Dec. 1991, IEEE Comput. Soc. Press, pp. 64-73.
[20] R. A. Marie, "An approximate analytical method for general queueing networks,"IEEE Trans. Software Eng., vol. 5, no. 5, pp. 530-538, Sept. 1979.
[21] T. Murata, "Petri nets: Properties, analysis, and applications,"Proc. IEEE, vol. 77, no. 4, pp. 541-580, Apr. 1989.
[22] M. Silva,Las Redes de Petri en la Automática y la Informática, Madrid: Editorial AC, 1985.

Index Terms:
Petri nets; stochastic processes; performance evaluation; approximate throughput computation; stochastic marked graphs; iterative technique; stochastic strongly connected marked graphs; net decomposition; single input-single output cut; qualitative behavior; general decomposition technique; iterative response time approximation method; error; state space; intractable systems; stochastic Petri net models
J. Campos, J.M. Colom, H. Jungnitz, M. Silva, "Approximate Throughput Computation of Stochastic Marked Graphs," IEEE Transactions on Software Engineering, vol. 20, no. 7, pp. 526-535, July 1994, doi:10.1109/32.297941
Usage of this product signifies your acceptance of the Terms of Use.